As India prepares to host the Group of 20 summit this week, the government of Prime Minister Narendra Modi raised eyebrows after an official invitation sent on behalf of the president used a different name for the country: Bharat.

A dinner invitation sent Tuesday to the visiting leaders of G20 countries described Droupadi Murmu as “President of Bharat” instead of “President of India.”

That decision was cheered by many Hindu nationalist leaders from Mr. Modi’s ruling Bharatiya Janata Party, who said it represented a rejection of the country’s colonial legacy (though “India” was widely used before the British set foot on the subcontinent).

But opposition groups have questioned the motivation and timing for using Bharat, which appeals to the prime minister’s Hindu nationalist base.

There were no immediate comments from Mr. Modi suggesting he would move to officially change the country’s name to Bharat. But the Indian news media was reporting late on Wednesday that his party might propose the change in a coming session of the federal Parliament.

Mr. Modi’s penchant for sudden political moves aimed at stirring up his supporters, including an abrupt ban on the country’s largest currency bills, has made him more popular with his base.

Bharat, originally a Sanskrit word, is the nation’s official name in Hindi, but in all communication in English and with other countries, the nomenclature is India. The country’s Constitution uses the term just once — “India, that is Bharat, shall be a Union of States,” Article 1 says — but that was enough for at least one government official.

“‘India, that is Bharat’ — it is there in the Constitution,” Subrahmanyam Jaishankar, India’s foreign minister, told a news agency on Wednesday. “Please, I would invite everybody to read it.”

The Constitution, however, refers to the nominal head of the country as the president of India.

The invitation controversy came days after Mohan Bhagwat, the chief of Rashtriya Swayamsevak Sangh, an organization that holds powerful sway over India’s Hindu right, said that people should use the name Bharat instead of India.